[Corrélation des polynômes d'Adomian et des polynômes de Bell exponentiels partiels]
Nous montrons des relations de récurrence entre les vecteurs partition des polynômes de Bell exponentiels partiels. Utilisant ces relations, le n-ième polynôme d'Adomian, pour n'importe quel opérateur non linéaire, s'exprime explicitement en termes des polynômes de Bell exponentiels partiels. On en déduit des identités nouvelles pour ces derniers, via la solution de certaines équations différentielles ordinaires, en utilisant la méthode de décomposition d'Adomian.
We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the n-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using the Adomian decomposition method.
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@article{CRMATH_2017__355_9_929_0,
author = {Kataria, Kuldeep Kumar and Vellaisamy, Palaniappan},
title = {Correlation between {Adomian} and partial exponential {Bell} polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {929--936},
publisher = {Elsevier},
volume = {355},
number = {9},
year = {2017},
doi = {10.1016/j.crma.2017.08.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.08.002/}
}
TY - JOUR AU - Kataria, Kuldeep Kumar AU - Vellaisamy, Palaniappan TI - Correlation between Adomian and partial exponential Bell polynomials JO - Comptes Rendus. Mathématique PY - 2017 SP - 929 EP - 936 VL - 355 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.08.002/ DO - 10.1016/j.crma.2017.08.002 LA - en ID - CRMATH_2017__355_9_929_0 ER -
%0 Journal Article %A Kataria, Kuldeep Kumar %A Vellaisamy, Palaniappan %T Correlation between Adomian and partial exponential Bell polynomials %J Comptes Rendus. Mathématique %D 2017 %P 929-936 %V 355 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.08.002/ %R 10.1016/j.crma.2017.08.002 %G en %F CRMATH_2017__355_9_929_0
Kataria, Kuldeep Kumar; Vellaisamy, Palaniappan. Correlation between Adomian and partial exponential Bell polynomials. Comptes Rendus. Mathématique, Tome 355 (2017) no. 9, pp. 929-936. doi : 10.1016/j.crma.2017.08.002. http://www.numdam.org/articles/10.1016/j.crma.2017.08.002/
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